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barbarian.]... Examinations are mysteries before which I bow.
Like the mysteries of theology, the reason must admit them
with humility, without seeking to understand them.11 As for
Galois, the failure was almost the finishing touch. It drove him
in upon himself and embittered him for life.
In 1828 Galois was seventeen. It was his great year. For the
first time he met a man who had the capacity to understand
his genius, Louis-Paul-Emile Richard (1795-1849), teacher of
advanced mathematics (mathematiques speciales) at Louis-le-
Grand. Richard was no conventional pedagogue, but a man of
talent who followed the advanced lectures on geometry at the
Sorbonne in his spare time and kept himself abreast of the
progress of living mathematicians to pass it on to his pupils.
Timid and unambitious on his own account, he threw all his
talent on the side of his pupils. The man who would not go a
step out of his way to advance his own interests counted no
Facrifice too great where the future of one of his students was
at stake. In his zeal to advance mathematics through the work
of abler men he forgot himself completely, although his scien-
tific friends urged him to write, and to his inspired teaching
more than one outstanding French mathematician of the nine-
teenth century has paid grateful tribute: Leverrier, co-disco-
verer with Adams by pure mathematical analysis of the planet
Xeptune; Serret, a geometer of repute and author of a classic
on higher algebra in which he gave the first systematic exposi-
tion of Galois' theory of equations; Hermite, master algebraist
and arithmetician of the first rank; and last, Galois.
Richard recognized instantly what had fallen into his hands -
kthe Abel of France'. The original solutions to difficult problems
which Galois handed in were proudly explained to the class,
with just praise for the young author, and Richard shouted
from the housetops that this extraordinary pupil should be
admitted to the Polytechnique without examination. He gave
Galois the first prize and wrote in his term report, This pupil
has a marked superiority above all his fellow students; he works
only at the most advanced parts of mathematics,' All of which
was the literal truth. Galois at seventeen was making disco-
veries of epochal significance in the theory of equations, dis-